graph the exponential function.\n\n$f(x)=(\\frac{5}{8})^x$\n\nplot five points on the graph of the function…

graph the exponential function.\n\n$f(x)=(\\frac{5}{8})^x$\n\nplot five points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

graph the exponential function.\n\n$f(x)=(\\frac{5}{8})^x$\n\nplot five points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

Answer

Explanation:

Step1: Find the y - intercept

Set (x = 0). Then (f(0)=\left(\frac{5}{8}\right)^0=1). So the point is ((0,1)).

Step2: Find another point for (x = 1)

When (x = 1), (f(1)=\frac{5}{8}=0.625). The point is ((1,0.625)).

Step3: Find a point for (x = 2)

When (x = 2), (f(2)=\left(\frac{5}{8}\right)^2=\frac{25}{64}\approx0.39). The point is ((2,\frac{25}{64})).

Step4: Find a point for (x=- 1)

When (x=-1), (f(-1)=\left(\frac{5}{8}\right)^{-1}=\frac{8}{5} = 1.6). The point is ((-1,1.6)).

Step5: Find a point for (x=-2)

When (x=-2), (f(-2)=\left(\frac{5}{8}\right)^{-2}=\left(\frac{8}{5}\right)^2=\frac{64}{25}=2.56). The point is ((-2,\frac{64}{25})). The general form of an exponential function (y = a^x) ((0\lt a\lt1) here (a=\frac{5}{8})) has a horizontal asymptote (y = 0).

Answer:

The five points are ((0,1)), ((1,0.625)), ((2,\frac{25}{64})), ((-1,1.6)), ((-2,\frac{64}{25})) and the horizontal asymptote is (y = 0).